Orbit Diagram of Two Coupled Logistic Maps

This Demonstration shows one orbit of the 2D coupled logistic map with 10,000 points. Using the slider controls you can vary the initial conditions of the orbit and the values of the two parameters of the system. Click the diagram to select an area of the orbit and see it magnified in the small window. Additional slider controls vary the degree of magnification in the small window and precision of the calculation.

THINGS TO TRY

SNAPSHOTS

DETAILS

The 2D coupled logistic map is given by the equations , .

This system exhibits chaotic behavior when and lie in the neighborhood of the region [1.032, 1.0843]. For certain ranges of the values of the parameters and the initial conditions, the dynamics can also converge to periodic orbits.